The current theory of the structure of the
Earth, called plate tectonics, tells us that the
continents are in constant motion.
Assume that the North American continent
can be represented by a slab of rock 5250 kmon a side and 35 km deep and that the rock
has an average mass density of 2630 kg/m3
.
The continent is moving at the rate of about
4.6 cm/year.
What is the mass of the continent?
Answer in units of kg.
mass=massdensity*L*W*depth
I would change all the lengths to meters first, to make the answer come out in kg.
Well, let's do some fun calculations, shall we? To find the volume of the continent slab, we can multiply its dimensions together:
Volume = length x width x height
Volume = 5250 km x 5250 km x 35 km
Now, we just need to convert the kilometers to meters, because physics likes meters better than kilometers.
Volume = 5250 km x 1000 m/km x 5250 km x 1000 m/km x 35 km x 1000 m/km
Volume = 5250 m x 5250 m x 35 m
Next, we can calculate the mass of the continent by multiplying the volume by the mass density:
Mass = Volume x density
Mass = (5250 m x 5250 m x 35 m) x 2630 kg/m³
And for the grand finale, let's include the motion of the continent:
Mass = [(5250 m x 5250 m x 35 m) x 2630 kg/m³] x (4.6 cm/year x 1 m/100 cm)
Now, let's not forget that the answer should be in kg, so let's simplify this whole mess to:
Mass = [(5250 x 5250 x 35 x 2630) x 4.6] / 1000
And the final answer comes out to be...
Drumroll, please...
Mass of North American continent = 2,020,305,125,000 kg
Now that's a whole lot of kgs!
To find the mass of the continent, we need to calculate the volume of the slab of rock and then multiply it by its density.
Step 1: Calculate the volume of the slab of rock
The volume (V) of a rectangular prism can be calculated using the formula:
V = length x width x height
Given:
Length = 5250 km
Width = 5250 km
Height = 35 km
Converting km to meters:
Length = 5250 km x 1000 m/km = 5,250,000 m
Width = 5250 km x 1000 m/km = 5,250,000 m
Height = 35 km x 1000 m/km = 35,000 m
Calculating the volume:
V = 5,250,000 m x 5,250,000 m x 35,000 m = 95,718,750,000,000,000 m^3
Step 2: Calculate the mass of the continent
The mass (m) of an object can be calculated using the formula:
m = density x volume
Given:
Density = 2630 kg/m^3
Volume = 95,718,750,000,000,000 m^3
Calculating the mass:
m = 2630 kg/m^3 x 95,718,750,000,000,000 m^3 = 2.519 x 10^20 kg
Answer:
The mass of the North American continent is approximately 2.519 x 10^20 kg.
To calculate the mass of the continent, you can use the formula:
Mass = volume x density
First, let's calculate the volume of the continent slab.
Given:
Length of slab (L) = 5250 km
Width of slab (W) = 5250 km
Depth of slab (D) = 35 km
Volume of slab = L x W x D
Since the dimensions are given in kilometers, we need to convert them to meters:
Length (L) = 5250 km = 5250 x 1000 = 5,250,000 meters
Width (W) = 5250 km = 5250 x 1000 = 5,250,000 meters
Depth (D) = 35 km = 35 x 1000 = 35,000 meters
Now, we can calculate the volume:
Volume of slab = 5,250,000 m x 5,250,000 m x 35,000 m
Next, we need to calculate the mass using the density:
Given:
Density (ρ) = 2630 kg/m^3
Mass = Volume x Density
Substituting the values:
Mass = (5,250,000 m x 5,250,000 m x 35,000 m) x 2630 kg/m^3
Now, calculate the mass using a calculator:
Mass ≈ 4.474 x 10^21 kg
Therefore, the mass of the North American continent is approximately 4.474 x 10^21 kilograms.